scholarly journals The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case

1990 ◽  
Vol 54 (190) ◽  
pp. 545 ◽  
Author(s):  
Bernardo Cockburn ◽  
Suchung Hou ◽  
Chi-Wang Shu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Conservation Laws ◽  
Discontinuous Galerkin ◽  
Multidimensional Case ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Local Projection ◽  
Discontinuous Galerkin Finite Element ◽  
Element Method

CONVERGENCE OF THE DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR HYPERBOLIC CONSERVATION LAWS

1995 ◽  
Vol 05 (03) ◽  
pp. 367-386 ◽  
Author(s):  
J. JAFFRE ◽  
C. JOHNSON ◽  
A. SZEPESSY
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Conservation Laws ◽  
Discontinuous Galerkin ◽  
Hyperbolic Conservation Laws ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Discontinuous Galerkin Finite Element ◽  
Systems Of Conservation Laws ◽  
Element Method

We prove convergence of the discontinuous Galerkin finite element method with polynomials of arbitrary degree q≥0 on general unstructured meshes for scalar conservation laws in multidimensions. We also prove for systems of conservation laws that limits of discontinuous Galerkin finite element solutions satisfy the entropy inequalities of the system related to convex entropies.

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